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Nejati, Ameneh; Soudjani, Sadegh; Zamani, Majid (2020): Compositional Construction of Control Barrier Functions for Networks of Continuous-Time Stochastic Systems. In: Ifac Papersonline, Vol. 53, No. 2: pp. 1856-1861
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In this paper, we propose a compositional framework for the construction of control barrier functions for networks of continuous-time stochastic control systems. The proposed scheme is based on a notion of so-called pseudo-barrier functions computed for subsystems, using which one can synthesize state-feedback controllers for interconnected systems enforcing safety specifications over a finite-time horizon. Particularly, we first leverage sufficient small-gain type conditions to compositionally construct control barrier functions for interconnected systems based on the corresponding pseudo-barrier functions computed for subsystems. Then, using the constructed control barrier functions, we quantify upper bounds on exit probabilities - the probability that an interconnected system reaches certain unsafe regions - in a finite-time horizon. We employ a systematic technique based on the sum-of-squares optimization program to search for pseudo-barrier functions of subsystems while synthesizing safety controllers. We demonstrate our proposed results by applying them to a temperature regulation in a network of 1000 rooms. Copyright (C) 2020 The Authors.